Lecture 4: Variance Estimation

Population Variance

The spread of the variable in the population

Sample variance

The spread of the variable in your sample

Sampling variance

How much an estimate varies across repeated samples

Sampling variability

How much a statistic differs from sample to sample, it is about precision and NOT bias

Standard Error

The standard deviation of the sampling distribution of an estimator

Confidence Interval

If we were to sample repeated, we would expect 95% of such constructed intervals to contain the population parameter

Precision

How closely repeated samples would give the same estimate (low sampling variability)

• Small Standard error/ Narrow confidence interval

Accuracy

Whether the estimate is unbiased or not

Bias

Systematic difference between the estimator’s expected value and the truth

When stratification helps most

When strata means differ a lot and units within a stratum are alike

Intra-cluster correlation (ρ)

How similar units in the same cluster are

Variance with clustering

Var = (σ²/N)[1 + (n-1)ρ]

• Rises with ρ and cluster size

Design Effect

Var(estimator under complex design) / var(estimator under SRSWOR)

Design Effect interpretation

A DEFF of x means x times as many SRSWOR observations are required to match the precision of the complex design.

Why cluster despite higher variance

There is no household list (only a list of clusters) and clusters cuts out the fieldwork and cost

Effect of design features

Weights affect bias and variance but clustering and stratification affect variance only